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Cardiovascular Mathematics

Modeling and simulation of the circulatory system

  • Book
  • © 2009

Overview

Editors:
  1. Luca Formaggia

    1. MOX, Department of Mathematics, Politecnico di Milano, Milan, Italy

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  2. Alfio Quarteroni

    1. MOX, Department of Mathematics, Politecnico di Milano, Milan, Italy
      CMCS-IACS, École Polytechnique Fédérale de Lausanne, Lausanne, Switzerland

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  3. Alessandro Veneziani

    1. MOX, Department of Mathematics, Politecnico di Milano, Milan, Italy
      Department of Mathematics and Computer Science, Emory University, Atlanta, USA

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Part of the book series: MS&A (MS&A, volume 1)

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Table of contents (12 chapters)

  1. Front Matter

    Pages I-XIII
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  2. Physiology and pathology of the cardiovascular system: A physical perspective

    • Marc Thiriet, Kim H. Parker
    Pages 1-45

  3. Basic mathematical models and motivations

    • Luca Formaggia, Karl Perktold, Alfio Quarteroni
    Pages 47-75

  4. The derivation of the equations for fluids and structure

    • Miguel A. Fernández, Luca Formaggia, Jean-Frédéric Gerbeau, Alfio Quarteroni
    Pages 77-121

  5. From image data to computational domains

    • Luca Antiga, Joaquim Peiró, David A. Steinman
    Pages 123-175

  6. Geometry and flow

    • Denis Doorly, Spencer Sherwin
    Pages 177-209

  7. Rheological models for blood

    • Anne M. Robertson, Adélia Sequeira, Robert G. Owens
    Pages 211-241

  8. Mathematical models of mass transfer in the vascular walls

    • Karl Perktold, Martin Prosi, Paolo Zunino
    Pages 243-278

  9. Analysis of coupled models for fluid-structure interaction of internal flows

    • Yvon Maday
    Pages 279-306

  10. Algorithms for fluid-structure interaction problems

    • Miguel A. Fernández, Jean-Frédéric Gerbeau
    Pages 307-346

  11. Reduced models of the cardiovascular system

    • Joaquim Peiró, Alessandro Veneziani
    Pages 347-394

  12. Multiscale models of the vascular system

    • Luca Formaggia, Alfio Quarteroni, Alessandro Veneziani
    Pages 395-446

  13. Applications and test cases

    • J. Alastruey Arimon, Denis Doorly, Sergio Giordana, Joaquim Peiró, Spencer Sherwin
    Pages 447-475

  14. Back Matter

    Pages 477-522
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Keywords

About this book

Cardiovascular diseases have a major impact in Western countries. Mathematical models and numerical simulations can aid the understanding of physiological and pathological processes, complementing the information provided to medical doctors by medical imaging and other non-invasive means, and opening the possibility of a better diagnosis and more in-depth surgical planning.This book offers a mathematically sound and up-to-date foundation to the training of researchers, and serves as a useful reference for the development of mathematical models and numerical simulation codes. It is structured into different chapters, written by recognized experts in the field, but it features a common thread with consistency of notation and expressions and systematic cross-referencing.

Editors and Affiliations

  • MOX, Department of Mathematics, Politecnico di Milano, Milan, Italy

    Luca Formaggia, Alfio Quarteroni, Alessandro Veneziani

  • CMCS-IACS, École Polytechnique Fédérale de Lausanne, Lausanne, Switzerland

    Alfio Quarteroni

  • Department of Mathematics and Computer Science, Emory University, Atlanta, USA

    Alessandro Veneziani

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